Zobrazeno 1 - 10
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pro vyhledávání: '"Kwon, Soonsik"'
Autor:
Kwak, Beomjong, Kwon, Soonsik
In this paper, we study the local well-posedness of nonlinear Schr\"odinger equations on tori $\mathbb{T}^{d}$ at the critical regularity. We focus on cases where the nonlinearity $|u|^{a}u$ is non-algebraic with small $a>0$. We prove the local well-
Externí odkaz:
http://arxiv.org/abs/2411.17147
We construct finite energy blow-up solutions for the radial self-dual Chern-Simons-Schr\"odinger equation with a continuum of blow-up rates. Our result stands in stark contrast to the rigidity of blow-up of $H^{3}$ solutions proved by the first autho
Externí odkaz:
http://arxiv.org/abs/2409.13274
Autor:
Kim, Taegyu, Kwon, Soonsik
We consider soliton resolution for the Calogero--Moser derivative nonlinear Schr\"odinger equation (CM-DNLS). A rigorous PDE analysis of (CM-DNLS) was recently initiated by G\'erard and Lenzmann, who demonstrated its Lax pair structure. Additionally,
Externí odkaz:
http://arxiv.org/abs/2408.12843
We consider the Calogero--Moser derivative nonlinear Schr\"odinger equation (CM-DNLS), which is an $L^{2}$-critical nonlinear Schr\"odinger equation with explicit solitons, self-duality, and pseudo-conformal symmetry. More importantly, this equation
Externí odkaz:
http://arxiv.org/abs/2404.09603
In this paper, we consider the asymptotic behaviors of small solutions to the semi-relativistic Hartree equations in two dimension. The nonlinear term is convolved with the Coulomb potential 1/|x|, and it produces the long-range interaction in the se
Externí odkaz:
http://arxiv.org/abs/2307.15886
In this paper, we consider the Maxwell-Dirac system in 3 dimension under zero magnetic field. We prove the global well-posedness and modified scattering for small solutions in the weighted Sobolev class. Imposing the Lorenz gauge condition, (and taki
Externí odkaz:
http://arxiv.org/abs/2208.12040
We consider the self-dual Chern-Simons-Schr\"odinger equation (CSS) under equivariant symmetry, which is a $L^{2}$-critical equation. It is known that (CSS) admits solitons and finite-time blow-up solutions. In this paper, we show soliton resolution
Externí odkaz:
http://arxiv.org/abs/2202.07314
Autor:
Kwon, Soonsik
Publikováno v:
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Thesis (Ph. D.)--UCLA, 2008.
Vita. Includes bibliographical references (leaves 71-73).
Vita. Includes bibliographical references (leaves 71-73).
Externí odkaz:
http://proquest.umi.com/pqdweb?did=1619605911&sid=1&Fmt=2&clientId=1564&RQT=309&VName=PQD
We consider the finite-time blow-up dynamics of solutions to the self-dual Chern-Simons-Schr\"odinger (CSS) equation (also referred to as the Jackiw-Pi model) near the radial soliton $Q$ with the least $L^{2}$-norm (ground state). While a formal appl
Externí odkaz:
http://arxiv.org/abs/2010.03252
Autor:
Kim, Kihyun, Kwon, Soonsik
Publikováno v:
Ann. PDE 9 (2023), no. 1, Paper No. 6, 129 pp
We consider the self-dual Chern-Simons-Schr\"odinger equation (CSS) under equivariance symmetry. Among others, (CSS) has a static solution $Q$ and pseudoconformal symmetry. We study the conditional stability of pseudoconformal blow-up solutions $u$ s
Externí odkaz:
http://arxiv.org/abs/2009.02943